[hist-analytic] Elizabeth Anscombe's Intention (New "Look Inside" feature)

Roger Bishop Jones rbj at rbjones.com
Wed Jun 16 15:51:09 EDT 2010

On Wednesday 16 Jun 2010 17:27, you wrote:
> Amazon has introduced the "Look Inside" feature of my
>  book _Elizabeth Anscombe's Intention_. 

Looks good!

> One thing on my mind as I do some
>  math needed for economics is the idea of a Limit in
>  calculus. You can simply substitute 'a' for 'x' in Lim
>  f(x) when f(a) is defined;
> x->a
> That is,
> Lim f(x) = fa
> x -> a

This is a definition of continuity, it won't hold, even if 
f(a) is defined, if there is a discontinuty at a.
Also, there may not be a limit either,
Lim f(x)
x -> a
does not always exist.

> But it is defined when x goes to a, where *a* is never
>  reached.

The limit may then be defined, but won't necessarily = f(a) 
and definitely won't, of course, if f is not defined at a. 

>  So the limit may be defined even when 'a'
>  doesn't exist (as what x goes to), or so it seems.

I presume you mean here f is not defined at a, rather than 
that a does not exist.

> My concern here is that quantification, e.g. UG, may be
>  possible where a does not exist.

This doesn't happen in any logic I know of, i.e. you only 
quantify over things which do exist.
(I dare say if you were keen you could formalise a 
Meinongian logic in which unusual things happen.)

However, you can write something like:

for all x such that P x then Q x.

which is a way of quantifying over P's whether or not there 
are any.
In that case you might say, if P is always false, that you 
have quantified over something which does not exist, though I 
think that's a confusing way of putting it.  Really you did 
a restricted quantification the effect of which was to 
quantify over nothing.

Roger Jones

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